Question

Solve the system of equations. 5x – 4y = –44 and –x + 3y = 22

Answer 1

To solve the system of equations, we have:

1. \( 5x - 4y = -44 \) (Equation 1)
2. \( -x + 3y = 22 \) (Equation 2)

We can solve this system using the substitution or elimination method. Here, I will use the substitution method.

First, let's solve Equation 2 for \(x\):

\[
-x + 3y = 22
\]
\[
-x = 22 - 3y
\]
\[
x = 3y - 22 \quad \text{(Equation 3)}
\]

Now we can substitute Equation 3 into Equation 1:

\[
5(3y - 22) - 4y = -44
\]

Expanding this gives:

\[
15y - 110 - 4y = -44
\]

Combining like terms:

\[
11y - 110 = -44
\]

Next, we add 110 to both sides:

\[
11y = 66
\]

Now divide by 11:

\[
y = 6
\]

Now we have the value of \(y\). We can substitute \(y\) back into Equation 3 to find \(x\):

\[
x = 3(6) - 22
\]
\[
x = 18 - 22
\]
\[
x = -4
\]

Thus, the solution to the system of equations is:

\[
x = -4, \quad y = 6
\]

The solution can be written as the ordered pair \((-4, 6)\).